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Simplifying 2a2 + 7a + -6 = 0 Reorder the terms: -6 + 7a + 2a2 = 0 Solving -6 + 7a + 2a2 = 0 Solving for variable 'a'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3 + 3.5a + a2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 3.5a + 3 + a2 = 0 + 3 Reorder the terms: -3 + 3 + 3.5a + a2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3.5a + a2 = 0 + 3 3.5a + a2 = 0 + 3 Combine like terms: 0 + 3 = 3 3.5a + a2 = 3 The a term is 3.5a. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5a + 3.0625 + a2 = 3 + 3.0625 Reorder the terms: 3.0625 + 3.5a + a2 = 3 + 3.0625 Combine like terms: 3 + 3.0625 = 6.0625 3.0625 + 3.5a + a2 = 6.0625 Factor a perfect square on the left side: (a + 1.75)(a + 1.75) = 6.0625 Calculate the square root of the right side: 2.46221445 Break this problem into two subproblems by setting (a + 1.75) equal to 2.46221445 and -2.46221445.Subproblem 1
a + 1.75 = 2.46221445 Simplifying a + 1.75 = 2.46221445 Reorder the terms: 1.75 + a = 2.46221445 Solving 1.75 + a = 2.46221445 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + a = 2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + a = 2.46221445 + -1.75 a = 2.46221445 + -1.75 Combine like terms: 2.46221445 + -1.75 = 0.71221445 a = 0.71221445 Simplifying a = 0.71221445Subproblem 2
a + 1.75 = -2.46221445 Simplifying a + 1.75 = -2.46221445 Reorder the terms: 1.75 + a = -2.46221445 Solving 1.75 + a = -2.46221445 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + a = -2.46221445 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + a = -2.46221445 + -1.75 a = -2.46221445 + -1.75 Combine like terms: -2.46221445 + -1.75 = -4.21221445 a = -4.21221445 Simplifying a = -4.21221445Solution
The solution to the problem is based on the solutions from the subproblems. a = {0.71221445, -4.21221445}
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